Disbelief~
If you don't have proof, and the OM is kind of being a jerk and dumping her, and from what you *CAN* see the A is over...then there is no point in exposing it because no A is going on. The reason you expose is to end the affair and so it's no longer a secret while they go around blaming you for their choice.
If "the love of her life" is dumping her (that's the way she sort of views it) then it seems normal that she'd be sad about that and walk around moping and depressed. If she says stuff about separating, I would suggest a stall tactic such as "it's the Holidays now and I'd really rather not make big moves and changes during the Holidays. Would you consider just putting off this action until the beginning of the year?" "May I make the request that we agree to get through this one last Holiday Season and then start the new year off fresh in a new way at that time?" or if she is really adamant, ask if she'd be willing to move to a guest bedroom "until the Holidays are over." This tactic just gives her a little time apart from the OM (out from under his sway) and give YOU a little time to really shine and show her that choosing she could build love and happiness at home--with the father of her children. (And FYI, you're not stalling with no intent to be cooperative after the holidays or in the new year...just asking for time to put off this major life decision.)
THEN during the stall time period it is VITAL...I mean life-and-death vital--for you to work on yourself, go to counseling if need be, be the father who takes the kids ice skating, etc. Right this second she remembers the really bad stuff right before the affair, and that's what she associates with you...so show her some good stuff. STOP all Love Extinguishers (you'd want to be that kind of person anyway). Get a life and enjoy your children--and let her enjoy them with you! Away from the OM and seeing you being the man you can be it is conceivable she may start to have some hope, and I believe it's your best chance.
Regarding her parents, I am not positive I would go there right this minute. Based on what you write, the A is not going on and she may just need some time to recover from being dumped. So if she agrees to stall and stays home, just be vigilant and have that in mind. If it's possible, they aren't in contact, and she's at home let's see what happens. If she does INSIST on moving out, then I would indeed tell the parents but as factually as possible: "I am so sorry to have to tell you but I thought you should know--dear wife has chosen to move out again and she and I are separating. The truly upsetting part is that I do have proof that she was involved in an affair that her other man ended, and I think the affair is strongly influencing her thinking. I do have evidence if you need to see it, and I've been in touch with the other man's spouse to confirm it, but I don't want to embarrass her--I just think it's relevant to the decision. So the kids and I will be living at home hoping she will decide to return to the family, and she will be living at XXX."